Estimating the properties of bone phantom cylinders through the inversion of axially transmitted low-frequency ultrasonic guided waves

Abstract

Early detection of osteoporosis has increasingly focused on ultrasonic methods, particularly guided waves in axial transmission to assess cortical bone properties. This study demonstrates the potential of low-frequency measurements ($<$500 kHz) for accurately inferring cortical mechanical and geometrical properties. A custom ultrasonic transducer centered at 350 kHz was used to acquire data, processed via a 2D fast Fourier transform to obtain dispersion curves. These were compared with simulations generated using the semi-analytical iso-geometric analysis (SAIGA) method, modeling a quasi-cylindrical bone geometry in void or immersed in olive oil. By incorporating an excitability parameter into the inversion algorithm, the proposed method achieved a less than 5% discrepancy between bone phantom properties determined via SAIGA inversion and bulk wave pulse-echo measurements, demonstrating its accuracy and potential for in vivo applications. Results also showed that high-wavenumber modes predominantly reflect material properties, whereas low-wavenumber modes below 100 kHz are sensitive to the overall bone geometry, highlighting the importance of low frequencies for a global bone characterization.